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Two-Way Substitutable Inventory System with N–Policy
Abstract
This article presents a two commodity stochastic inventory system under continuous review. The maximum storage capacity for the i-th item is fixed as Si (i = 1, 2). It is assumed that demand for the i-the commodity is of unit size and demand time points form Poisson distribution with parameter i = 1, 2. The reorder level is fixed as si for the i-th commodity (i = 1, 2) and the ordering policy is to place order for items for the i-th commodity (i = 1, 2) when both the inventory levels are less than or equal to their respective reorder levels. The lead time is assumed to be exponential. The two commodities are assumed to be substitutable. That is, if the inventory level of one commodity reaches zero, then any demand for this commodity will be satisfied by the item of the other commodity. If no substitute is available, then this demand is backlogged up to a certain level Ni, (i = 1, 2) for the i-th commodity. Whenever the inventory level reaches Ni, (i = 1, 2), an order for Ni items is replenished instantaneously. For this model, the limiting probability distribution for the joint inventory levels is computed. Various operational characteristics and expression for long run total expected cost rate are derived.
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